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Most independent component analysis methods for blind source separation rely on the fundamental assumption that all the unknown sources are mutually statistically independent. Such assumption becomes problematic when applied to many real world applications (e.g., biomedical imaging) that subsequently motivated the exploitation of non-negative nature of the sources, observations and mixing matrix. We recently proposed a new method, called the non-negative least-correlated component analysis (nLCA) for a noise-free 2 x 2 mixing system, that relaxes the source independence assumption while uses the non-negativity constraints on the sources, observations and mixing matrix. In this paper, we extend the nLCA to the case of a noisy M x N non-negative mixing system where M gesN ges 2. The nLCA involves only low-complexity algebraic computations, and thus is computationally efficient. Illustrative experimental results are presented to demonstrate its efficacy together with a performance comparison with some existing algorithms.